30 Faiga o le thermodynamics Isobaric – faʻafitauli ma fofo
1. O le ata PV o loʻo i lalo o loʻo faʻaalia ai se kasa lelei o loʻo ui atu i se faiga iso baric . Faʻatatau le galuega e faia e le kasa i le faiga AB.
Ua iloa:
Mamafa (P) = 5 x 10 5 N/m 2
Voluma muamua (V 1 ) = 2 m 3
Voluma mulimuli (V 2 ) = 6 m 3
Sailia: Galuega (W)
Fofo:
W = P (V 2 – V 1 )
W = (5 x 10 5 )(6 – 2) = (5 x 10 5 ) (4)
W = 20 x 10 5 = 2 x 10 6 Joules
2. O le a le eseesega o le galuega e faia e le kesi i le faagasologa AB ma le faagasologa CD…
Ua iloa:
Fa'agasologa Isobaric AB :
Mamafa (P) = 6 atm = 6 x 105 N / m2
Voluma muamua (V 1 ) = 1 lita = 1 dm 3 = 1 x 10 -3 m 3
Voluma mulimuli (V 2 ) = 3 lita = 3 dm 3 = 3 x 10 -3 m 3
Fa'agasologa Isobaric CD :
Mamafa (P) = 4 atm = 4 x 105 N / m2
Voluma muamua (V 1 ) = 2 lita = 2 dm 3 = 2 x 10 -3 m 3
Voluma mulimuli (V 2 ) = 5 lita = 5 dm 3 = 5 x 10 -3 m 3
Manaomia : O le eseesega o le galuega e faia e le kesi i le faagasologa AB ma le CD.
Fofo:
E faia le galuega e le kesi i le faagasologa AB:
W = P (V 2 – V 1 )
W = (6 x 10 5 )(3 x 10 -3 – 1 x 10 -3 )
W = (6 x 10 5 )(2 x 10 -3 )
W = 12 x 102 = 1200 Joule
E faia le galuega e le kesi o loʻo i totonu o le faagasologa CD:
W = P (V 2 – V 1 )
W = (4 x 10 5 )(5 x 10 -3 – 2 x 10 -3 )
W = (4 x 10 5 )(3 x 10 -3 )
W = 12 x 102 = 1200 Joule
O le eseesega o le galuega e faia e le kesi i le faagasologa AB ma le CD = 1200 – 1200 = 0.
3. O le galuega e faia e le kesi i le faagasologa o le ABC o le….
Ua iloa:
Mamafa 1 (P 1 ) = 6 x 10 5 Pa = 6 x 10 5 N/m 2
Mamafa 2 (P 2 ) = 3 x 10 5 Pa = 3 x 10 5 N/m 2
Voluma 1 (V 1 ) = 2 cm 3 = 2 x 10 -6 m 3
Voluma 2 (V 2 ) = 6 cm 3 = 6 x 10 -6 m 3
Manaomia : O le galuega ua maeʻa i le faagasologa ABC.
Fofo:
I le faagasologa AB, e tausia le voluma e tutusa ina ia leai se galuega e faia e le kesi.
Sa faia le galuega e le kesi i le faagasologa BC.
W = P 2 (V 2 – V 1 )
W = (3 x 10 5 )(6 x 10 -6 – 2 x 10 -6 )
W = (3 x 10 5 )(4 x 10 -6 )
W = 12 x 10 -1
W = 1.2 Joule
O le galuega e faia i le faagasologa ABC = o le galuega e faia i le faagasologa AB = 1.2 Joules.
4. Fuafua le suiga o le malosiaga i totonu mo le 2 moles o se kasa lelei o loʻo faia se faʻalauteleina isobaric i le 300 K, lea \(\Delta V = 1\ \text{m}^3\).
Tali: \(\Delta U = nC_v\Delta T\), fa'aaoga le \(C_v = \frac{R}{\gamma-1}\) (mo le kasa lelei monatomic, \(\gamma = \frac{5}{3}\)) ma le \(\Delta T = \frac{P\Delta V}{nR}\), \(\Delta U = \frac{2\cdot 300 \cdot 1}{\frac{5}{3}-1} \approx 1800\ \text{J}\).
5. Fuafua le fesiitaiga o le vevela i se faiga isobaric lea e fa’alauteleina ai le 1 mole o se kasa diatomic ideal, \(C_p = \frac{7}{2}R\), ma le \(\Delta T = 50\ \text{K}\).
Tali: \(Q = nC_p\Delta T = \frac{7}{2} \cdot 50 \cdot R \approx 1750\ \text{J}\) (fa'aaogaina \(R = 8.314\ \text{J/(mol·K)}\)).
6. Saili le galuega na faia e se faiga o loʻo faia se faʻalauteleina isobaric, \(P = 3\ \text{atm}\), \(\Delta V = 4\ \text{L}\).
Tali: \(W = P\Delta V = 3 \times 4 = 12\ \text{L·atm}\).
7. Fuafua le suiga i le entropy mo se faiga isobaric lea e suia ai e le 2 moles o se kasa lelei le vevela i le 20 K. Faaaoga le \(C_p = \frac{5}{2}R\).
Tali: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 2 \cdot \frac{5}{2}R \cdot \ln\frac{T_1+20}{T_1}\).
8. Fuafua le fesiitaiga o le vevela mo se fa'apipi'iina isobaric o se kasa lelei monatomic, \(C_p = \frac{5}{2}R\), \(\Delta T = -10\ \text{K}\).
Tali: \(Q = nC_p\Delta T = \frac{5}{2} \cdot (-10) \cdot R \approx -415\ \text{J}\).
9. Saili le galuega na faia i luga o le faiga i se faiga isobaric ma le \(P = 5\ \text{bar}\), \(\Delta V = -3\ \text{m}^3\).
Tali: \(W = P\Delta V = 5 \times (-3) = -15\ \text{bar m}^3\).
10. Fuafua le suiga i le malosiaga i totonu mo se faiga isobaric lea \(n = 3\ \text{mol}\), \(C_v = 3R\), \(\Delta T = 25\ \text{K}\).
Tali: \(\Delta U = nC_v\Delta T = 3 \cdot 3R \cdot 25 \approx 1883\ \text{J}\).
11. Fuafua le suiga o le entropy i se faiga isobaric mo se kasa lelei diatomic, \(n = 1\ \text{mol}\), \(\Delta T = 40\ \text{K}\), \(T_1 = 300\ \text{K}\).
Tali: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = \frac{7}{2}R\ln\frac{340}{300}\).
12. Saili le fesiitaiga o le vevela i totonu o se fa'alauteleina isobaric, \(P = 2\ \text{atm}\), \(\Delta V = 3\ \text{L}\), \(C_p = \frac{7}{2}R\).
Tali: \(Q = P\Delta V + nC_p\Delta T = 2 \times 3 + \frac{7}{2}R\Delta T\).
13. Fuafua le galuega na faia i se faiga isobaric mo \(P = 4\ \text{bar}\), \(\Delta V = 5\ \text{m}^3\).
Tali: \(W = P\Delta V = 4 \times 5 = 20\ \text{bar m}^3\).
14. Fuafua le suiga o le malosiaga i totonu mo se fa'apipi'iga isobaric, \(n = 2\ \text{mol}\), \(C_v = \frac{3}{2}R\), \(\Delta T = -30\ \text{K}\).
Tali: \(\Delta U = nC_v\Delta T = 2 \cdot \frac{3}{2}R \cdot (-30) \approx -753\ \text{J}\).
15. Saili le suiga o le entropy i se faiga isobaric, \(n = 1.5\ \text{mol}\), \(\Delta T = 60\ \text{K}\), \(T_1 = 400\ \text{K}\), \(C_p = \frac{5}{2}R\).
Tali: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 1.5 \cdot \frac{5}{2}R\ln\frac{460}{400}\).
16. Fuafua le fesiitaiga o le vevela mo se fa'alauteleina isobaric, \(P = 3\ \text{bar}\), \(\Delta V = 2\ \text{m}^3\), \(C_p = \frac{5}{2}R\), \(n = 2\ \text{mol}\).
Tali: \(Q = P\Delta V + nC_p\Delta T = 3 \times 2 + 2 \cdot \frac{5}{2}R\Delta T\).
17. Fuafua le galuega e faia i luga o le 3 moles o se kasa o loʻo faia se isobaric compression, \(P = 5\ \text{atm}\), \(\Delta V = -4\ \text{L}\).
Tali: \(W = P\Delta V = 5 \times (-4) = -20\ \text{L·atm}\).
18. Fuafua le suiga o le malosi i totonu mo \(n = 4\ \text{mol}\), \(C_v = \frac{7}{2}R\), \(\Delta T = 15\ \text{K}\) i se faiga isobaric.
Tali: \(\Delta U = nC_v\Delta T = 4 \cdot \frac{7}{2}R \cdot 15 \approx 3157\ \text{J}\).
19. Saili le fesiitaiga o le vevela i se faiga isobaric, \(P = 4\ \text{atm}\), \(\Delta V = 5\ \text{L}\), \(n = 2\ \text{mol}\), \(C_p = \frac{5}{2}R\).
Tali: \(Q = P\Delta V + nC_p\Delta T = 4 \times 5 + 2 \cdot \frac{5}{2}R\Delta T\).
20. Fuafua le galuega e faia i le fa'apipi'iina o le isobaric, \(P = 7\ \text{bar}\), \(\Delta V = -2\ \text{m}^3\).
Tali: \(W = P\Delta V = 7 \times (-2) = -14\ \text{bar m}^3\).
21. Fuafua le suiga o le malosiaga i totonu mo le 3 mole o se kasa lelei o loʻo faia i se faiga isobaric, \(C_v = \frac{5}{2}R\), \(\Delta T = 20\ \text{K}\).
Tali: \(\Delta U = nC_v\Delta T = 3 \cdot \frac{5}{2}R \cdot 20 \approx 1256\ \text{J}\).
22. Saili le suiga o le entropy mo se fa'alauteleina isobaric, \(n = 1\ \text{mol}\), \(C_p = \frac{7}{2}R\), \(\Delta T = 30\ \text{K}\), \(T_1 = 250\ \text{K}\).
Tali: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = \frac{7}{2}R\ln\frac{280}{250}\).
23. Fuafua le fesiitaiga o le vevela i se faiga isobaric, \(P = 6\ \text{bar}\), \(\Delta V = 4\ \text{m}^3\), \(n = 3\ \text{mol}\), \(C_p = \frac{3}{2}R\).
Tali: \(Q = P\Delta V + nC_p\Delta T = 6 \times 4 + 3 \cdot \frac{3}{2}R\Delta T\).
24. Fuafua le galuega na faia e le faiga i se fa'alautelega isobaric ma le \(P = 8\ \text{bar}\), \(\Delta V = 3\ \text{m}^3\).
Tali: \(W = P\Delta V = 8 \times 3 = 24\ \text{bar m}^3\).
25. Fuafua le suiga o le malosiaga i totonu mo se faiga isobaric lea \(n = 2\ \text{mol}\), \(C_v = \frac{7}{2}R\), \(\Delta T = -10\ \text{K}\).
Tali: \(\Delta U = nC_v\Delta T = 2 \cdot \frac{7}{2}R \cdot (-10) \approx -878\ \text{J}\).
26. Saili le suiga o le entropy mo se kasa lelei diatomic i totonu o se fa'apipi'iga isobaric, \(n = 1.5\ \text{mol}\), \(T_1 = 350\ \text{K}\), \(\Delta T = -40\ \text{K}\).
Tali: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 1.5 \cdot \frac{7}{2}R\ln\frac{310}{350}\).
27. Fuafua le fesiitaiga o le vevela mo le 2 mole o se kesi o loʻo faia se faʻalauteleina isobaric, \(P = 5\ \text{bar}\), \(\Delta V = 6\ \text{m}^3\), \(C_p = \frac{5}{2}R\).
Tali: \(Q = P\Delta V + nC_p\Delta T = 5 \times 6 + 2 \cdot \frac{5}{2}R\Delta T\).
28. Fuafua le galuega na faia i luga o le faiga i se fa'apipi'iga isobaric ma le \(P = 9\ \text{atm}\), \(\Delta V = -3\ \text{L}\).
Tali: \(W = P\Delta V = 9 \times (-3) = -27\ \text{L·atm}\).
29. Fuafua le suiga o le malosiaga i totonu mo le 3 mole o se kasa o loʻo faia i se faiga isobaric, \(C_v = \frac{3}{2}R\), \(\Delta T = 15\ \text{K}\).
Tali: \(\Delta U = nC_v\Delta T = 3 \cdot \frac{3}{2}R \cdot 15 \approx 564\ \text{J}\).
30. Saili le suiga o le entropy i se fa'alauteleina isobaric, \(n = 4\ \text{mol}\), \(C_p = \frac{5}{2}R\), \(\Delta T = 25\ \text{K}\), \(T_1 = 300\ \text{K}\).
Tali: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 4 \cdot \frac{5}{2}R\ln\frac{325}{300}\).
